restriction of a function (original) (raw)
Definition
Let f:X→Y be a function from a set X to a set Y. If A is a subset of X, then the restriction of f to A is the function
| f|A:A | → | Y |
|---|---|---|
| x | ↦ | f(x). |
Some authors write f↾A instead of f|A.
Properties
If A⊆X, and B⊆Y, then
| (f|A)-1(B) | = | A∩f-1(B). |
|---|
| Title | restriction of a function |
|---|---|
| Canonical name | RestrictionOfAFunction |
| Date of creation | 2013-03-22 13:43:05 |
| Last modified on | 2013-03-22 13:43:05 |
| Owner | yark (2760) |
| Last modified by | yark (2760) |
| Numerical id | 14 |
| Author | yark (2760) |
| Entry type | Definition |
| Classification | msc 03E20 |
| Synonym | restriction |
| Related topic | Pullback2 |
| Related topic | ExtensionOfAFunction |